Compared to traditional x-ray absorption radiography, phase radiography is better suited for visualizing soft-tissue structures which do not appreciably absorb x-rays, but which may contain non-absorptive structural details. Internal structures may produce a measurable deviation in the direction and velocity of the incident radiation because of local variations in the refractive index, and variations in density and thickness of those structures. Phase disturbances occur at interfaces between soft-tissue planes that have slightly different refractive indices and thicknesses. Within soft-tissues, incident radiation is refracted by spatially oriented molecular and atomic planes, thereby experiencing a significant shift in phase, corresponding to a change in direction.
For hard x-rays, the cross section for absorption, which generates the contrast in conventional radiography, is usually much smaller than that for elastic scattering. The elastic scattering causes a phase shift of the wave passing through matter. Thus, the possibility to record the elastic scattering and phase shift of x-rays opens the potential for greatly enhanced contrast and, in consequence, reduction of the applied x-ray dose. Reduction of the dose is desirable i) because of health risks for patients exposed to x-rays, and ii) because of the reduced exposure times.
Several methods to detect phase variations in the radiation behind the sample were developed in the past years. They can be classified into interferometric methods, techniques using an analyzer crystal, and free-space propagation methods. These methods differ in the nature of the signal recorded, the experimental setup, and the requirements on the illuminating radiation (especially its spatial coherence and monochromaticity). Many experimental results known in the prior art were obtained at synchrotron x-ray sources, which are highly expensive installations and are only available at distinct scientific facilities. The commercial impact of an invention in context with radiography will greatly depend on whether an x-ray tube is suitable as radiation source or whether the method is restricted to use at synchrotron radiation facilities because of the required degree of coherence.
The use of gratings as optical elements in hard x-ray phase imaging has shown the potential of overcoming the problems that so far impair the wider use of phase contrast in x-radiography and tomography. Several different geometries of grating-based interferometers for hard x-rays have been investigated recently.
The Talbot-Lau self-imaging effect, i.e., its replication in the longitudinal direction without the use of a lens, has been widely studied and used for a number of applications, including x-ray phase imaging and x-ray dark-field scatter imaging. Talbot self-imaging can be described in the following way: a (quasi-)monochromatic wavefield of wavelength λ with lateral period 1/v1 is also longitudinally periodic. The longitudinal period zT—often referred to as the Talbot-distance—is given as zT=2/λv12. A common practical implementation of the Talbot effect is achieved when one 1D grating is illuminated by x-rays proceeding from a monochromatic spatially coherent point source and the grating pattern is replicated at certain far-field distances.
The Lau effect is the spatially incoherent counterpart of the Talbot effect. The Lau effect is obtained when one allows the superposition in consonance of Talbot fringes generated by a series of mutually incoherent quasi-monochromatic sources. A common practical implementation of the Lau effect is achieved when two 1D gratings, oriented parallel to each other, are illuminated by the x-rays proceeding from a quasi-monochromatic spatially incoherent planar source, and the grating pattern is replicated at certain far-field distances.
The second grating divides the incoming beam essentially into the two first diffraction orders. The angle between the two diffracted beams is so small that they overlap almost completely. In the overlap region downstream of the second grating, the diffracted beams interfere and form linear periodic fringe patterns in planes perpendicular to the optical axis, at a Talbot distance down-stream of the second grating.
The period of the x-ray interference pattern is usually in the range of a few microns, which can only be conveniently resolved by a very high resolution detector in combination with a very intense illumination and hence, limits the field-of-view significantly. For this reason, an analyzer grating, typically an absorption grating, is placed at a fractional Talbot length to analyze the interference pattern. The analyzer grating, normally having the same period as the self-imaged interference fringes, can be scanned in the transverse direction in a technique called “phase-stepping.” An alternative approach is the retrieval of the differential phase by using Moiré fringes when inclining the analyzer grating against the source gratings. Large-format x-ray gratings with high aspect ratios and small periods are difficult to fabricate and do not efficiently use x-rays from laboratory sources.
A publication (PCT WO 2011/011014 A1), discloses a scattering imaging method using an intensity modulating grid, which is easier to fabricate than a diffractive grating. A detector captures a raw image of the modulated intensity pattern. A comparative Fourier Transform analysis method is used to obtain both a scattering image and a phase-contrast image from the detected modulated intensity pattern. The disclosed comparative Fourier Transform analysis method of PCT WO 2011/011014 A1 is hereby reference in full. However, the overall described method (PCT WO 2011/011014 A1) does not allow for slight shifts in phase and ultra small angle scattering as the simple shadowgraph image acquisition method is limited in the grid-pitch and grid-to-detector distance. Also, the method (PCT WO 2011/011014 A1) requires sample movement and/or intensity variation during exposure to remove analytical confusion from sharp-edge absorptive features in certain samples. Thus, the problems of the method (PCT WO 2011/011014 A1) make it unsuitable for phase and scattering imaging of many low density objects.
A technique, published by Doblas, et al, “Axial resonance of periodic patterns by using a Fresnel biprism” (J. Opt. Soc. Am. A/Vol. 30, No. 1/January 2013) formalizes the production of resonant fringes with a visible-light Fresnel biprism. That research, hereby reference in full, considered some possible alternatives, (such as the Wollaston prism, Lloyd's mirror and the Kösters prism) to the Fresnel biprism. That research did not discuss a Billet split lens, and did not discuss the use of x-radiation.
An alternative method in needed to produce high-contrast localized sinusoidal or stepped-intensity modulated patterns with spatially non-coherent illumination. A need also exist for an alternative method that would allow progressively increasing periods to allow for easier detection and analysis. Lastly, a need exist for a more efficient use of the radiation from a laboratory x-ray tube source.